Only official stuff will be transferred. Meaning stuff you didn't purchase from the Shop Channel (Homebrew channels) will stay on the old Wii. Once transferred over that's it, you will not be able to restore them to the first system unless you re-buy them.

What about just the Wii games' save files?
Can those be moved back and forth, or will my old system just be considered a fresh one?
I have a save file of a game I can't exactly play on a non-pal console.